RESEARCH ARTICLE10.1002/2015WR017626

Geomorphological control on variably saturated hillslopehydrology and slope instabilityFormetta Giuseppe1, Silvia Simoni2, Jonathan W. Godt3, Ning Lu1, and Riccardo Rigon4

1Department of Civil & Environmental Engineering, Colorado School of Mines, Golden Colorado, USA, 2Mountain-eeringSrl, Bolzano, Italy, 3U.S. Geological Survey, Golden Colorado, USA, 4Department of Civil and Environmental Engineering,University of Trento, Italy

Abstract In steep topography, the processes governing variably saturated subsurface hydrologicresponse and the interparticle stresses leading to shallow landslide initiation are physically linked. However,these processes are usually analyzed separately. Here, we take a combined approach, simultaneously ana-lyzing the influence of topography on both hillslope hydrology and the effective stress fields within the hill-slope itself. Clearly, runoff and saturated groundwater flow are dominated by gravity and, ultimately, bytopography. Less clear is how landscape morphology influences flows in the vadose zone, where transientfluxes are usually taken to be vertical. We aim to assess and quantify the impact of topography on both sat-urated and unsaturated hillslope hydrology and its effects on shallow slope stability. Three real hillslopemorphologies (concave, convex, and planar) are analyzed using a 3-D, physically based, distributed modelcoupled with a module for computation of the probability of failure, based on the infinite slope assumption.The results of the analyses, which included parameter uncertainty analysis of the results themselves, showthat convex and planar slopes are more stable than concave slopes. Specifically, under the same initial,boundary, and infiltration conditions, the percentage of unstable areas ranges from 1.3% for the planar hill-slope, 21% for convex, to a maximum value of 33% for the concave morphology. The results are supportedby a sensitivity analysis carried out to examine the effect of initial conditions and rainfall intensity.

1. Introduction

Shallow landslides often occur in steep terrains in response to intense or prolonged rainfall. The local curva-ture of the ground surface has an influence on landslide-related factors, such as steady state hydrology, ero-sion, sediment transport, and spatial variation of soil thickness [e.g., Heimsath et al., 1997; Dietrich et al.,2003; Dietrich and Montgomery, 1994]. To quantify the impact of topography on hillslope stability, one mustfirst identify the processes directly affected by topography and then understand the effects of these on hill-slope stability. In the short-term, topographic influence on landforming processes can be either time-dependent or time-independent. On the one hand, up to the landslide triggering point, topography, spatialvariations of soil depth, and material properties are essentially time-independent (of course, the stress fieldis influenced by transient infiltrations and redistributions). On the other hand, during the post failure phase,all of these aspects are time-dependent. In this paper, however, we are interested in the prefailure stages.

Topography mainly affects slope stability through two main processes: transient hillslope hydrology andsediment transport. Transient hydrology, described by the Richards [1931] equation, determines soil mois-ture changes and related variations in pore water pressure. Sediment transport and erosion determine soilthickness and the amount of sediment available for potential failure. The effect of topography on hydrologyhas been largely investigated with respect to saturated, subsurface flows. In these cases, topographicallydriven flows have been shown to generate spatial patterns of soil moisture and pore pressure distributionsthat play a significant role in shallow landslide triggering [Dietrich et al., 1986; D’Odorico and Rigon, 2003].Clearly, runoff and saturated groundwater flows are driven by gravity and, ultimately, by topography.Understanding whether the landscape morphology has a bearing on subsurface flows in the vadose zone,however, is less intuitive. To this end, Philip [1991b] carried out an infiltration analysis on a homogeneous,isotropic, planar slope. Having defined the downslope direction as slope parallel, he found that infiltrationalways generates a downslope subsurface flux component due to gravity. This component is time-dependent, being proportional to t1=2 in the short-term and to t in the long. Furthermore, Philip [1991a,

Key Points:� Quantify the impact of topography

on saturated-unsaturated hillslopehydrology and slope-stability� Morphology impact on transient

hydrology is not relevant at local butimportant at catchment scale� Percentage of unstable areas was 1.3

for planar, 21 for convex, and 33 forconvergent morphology

Supporting Information:� Supporting Information S1

Correspondence to:G. Formetta,giuseppe.formetta@unical.it

Citation:Giuseppe, F., S. Simoni, J. W. Godt,N. Lu, and R. Rigon (2016),Geomorphological control on variablysaturated hillslope hydrology andslope instability, Water Resour. Res., 52,4590–4607, doi:10.1002/2015WR017626.

Received 3 JUN 2015

Accepted 13 MAY 2016

Accepted article online 19 MAY 2016

Published online 18 JUN 2016

VC 2016. American Geophysical Union.

All Rights Reserved.

GIUSEPPE ET AL. GEOMORPHOLOGICAL CONTROL ON SLOPE INSTABILITY 4590

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1991c] shows that the results found for a planar slope can be extended to convex and concave slopes, pro-vided that the radius of curvature of the terrain surface is small compared to the characteristic infiltrationlength (about 10 times smaller). According to his work, perturbation effects generated by divergence/con-vergence on unsaturated subsurface flows are unimportant for usual hillslope topography.

A significant contribution to the understanding of infiltration in partially saturated soils was given by Iverson[2000]. He showed that, in the short-term, transient fluxes have a prevalent vertical component for pointswhere �5H=

ffiffiffiAp� 1, (H is the vertical soil depth and A is the upslope contributing area) [Iverson, 2000].

However, landslides and debris flows often occur as a consequence of complex interactions between verti-cal infiltrations and preexisting soil moisture patterns, the latter resulting from catchment-scale subsurfaceflows and geomorphological features in addition to variable rainfall inputs [D’Odorico and Rigon, 2003].

A debate arose regarding the actual existence of the downslope-upslope flow components. Lu et al. [2011]showed that within a homogeneous and isotropic hillslope, under time-varying rainfall conditions, verticaldownslope, and upslope lateral flows can occur concurrently in different points. In particular, unsaturated,downslope, lateral flow occurs if the point is in a ‘‘drying’’ state (@h@t < 0), while unsaturated, upslope, lateralflow occurs if the point is in a ‘‘wetting’’ state (@h@t > 0).

In partially saturated soils, an increase in moisture content due to rainfall infiltration and the consequentdecrease (absolute value) in pore water pressures reduce interparticle stresses. However, although transientinfiltration and reduction in soil stress are strictly connected, their effects are often analyzed separately instability analyses, and usually by assuming a steady state hydrological framework. Examples of physicallybased models within this context are SHALlow STABility analysis (SHALSTAB) [Dietrich and Montgomery,1994], dSLAM [Wu and Sidle, 1995], and Stability INdex MAPping (SINMAP) [Pack et al., 1998; Lanni et al.,2012]. These models couple a simple steady state or quasi-dynamic hydrology with an infinite-slope analysisfor the computation of the Factor of Safety (or stability index), defined as the ratio between stabilizing anddestabilizing forces [Taylor, 1948]. Analyses carried out with models based on the steady state hydrologyapproach do not account for the effects of transient hydrology. The distributed model TRIGRS [Baum et al.,2010], which uses one-dimensional, analytic, rainfall infiltration models for computing Factors of Safety, rep-resents an advance in this direction. Other examples of models based on the Richards equation approxima-tion, and thus capable of taking account of the transient, are presented in Capparelli and Versace [2011],Lepore et al. [2013], and Tsai and Yang [2006].

There are many studies [e.g., BeVille et al., 2010; Mirus et al., 2007; Simoni et al., 2008] that have combinedtwo-dimensional or three-dimensional, variably saturated, flow models with slope stability models. Shaoet al. [2015] coupled a two-dimensional, variably saturated hydrological model with a model for the compu-tation of the local factor of safety to investigate the influence of preferential flow on slope stability. Ebelet al. [2010] investigates the effects of the hysteretic nature of the soil-water retention curve on slope stabil-ity by coupling a three-dimensional, variably saturated, flow model with a one-dimensional slope stabilitymodel.

The effects of topographic curvature on landslide potential are qualitatively known and some applicationsusing empirical, landslide-susceptibility models have been presented [e.g., Dai and Lee, 2002; Carrara et al.,2003; Dahal et al., 2008]. However, to our knowledge, these effects have not been quantitatively assessedwith 3-D hydrological models.

This paper aims to investigate whether short-term water fluxes are affected by topography and, if so, towhat extent these effects influence slope stability at the catchment scale. We analyzed three real slope mor-phologies (concave, convex, and planar) using the 3-D, physically based, distributed hydrological modelGEOtop [Rigon et al., 2006; Simoni, 2007; Endrizzi et al., 2014] combined with a module to compute the prob-ability of failure, based on an infinite slope analysis. GEOtop computes water and energy balances dynami-cally and provides maps of soil moisture and pressure head at user-defined time steps. The stabilitymodule, FS, works in concert with GEOtop, carrying out stability analyses based on computed pressureheads and moisture contents. Finally, the probability of failure is computed using the First Order SecondMoment method [Dai and Lee, 2002; Baecher and Christian, 2005].

Results are given for each location and each time step in terms of: pressure head; water content; suctionstress; and probability of failure. The relationships between slope and pressure head, water content, and

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probability of failure, respectively, have been reported to highlight the influence of topography on instabil-ity. For the examples investigated here, it was seen that convex and planar slopes are generally more stablethan concave ones.

2. Analysis of the Physical Processes

2.1. Transient Hillslope HydrologyRainfall infiltration, and the consequent changes in pore-water pressure, control shallow landslide initiationin the short-term. Specifically, there are four rainfall attributes that, combined with soil hydraulic properties,strongly affect landslide triggering. These are: total amount of rainfall; antecedent storm precipitation; stormduration; and short-term rainfall intensity [Lu and Godt, 2013]. These factors have a direct influence on pore-pressure generation. Indeed, in analyzing the temporal variations in slope stability, one examines the role ofpore-water pressure on the stress state of the soil. The Richards [1931] equation describes three-dimensional infiltration and water redistribution processes in variably saturated porous media, and transientprocesses taking place in unsaturated soil in the shallow subsurface where rainfall infiltration occurs. TheRichards equation combines Darcy’s law (for a general theory of unsaturated-saturated flow in porousmedia see Bear [1972]) and the principle of mass conservation for an incompressible fluid;

r½�K ðhÞ � ~rðw2zÞ�5 @h@t

1S (1)

where �K ðhÞ is a generic 3 3 3 tensor describing the hydraulic conductivity [L/T], h is the volumetric watercontent [L3=L3], w is the pressure head or water potential [L], z is the vertical coordinate, positive downward[L], t is time, and S represents the sink term describing the specific water volumetric losses (root uptake,evapotranspiration, etc.) [T21]. Transient approaches to modeling slope stability in response to rainfall infil-tration typically try to solve this equation. However, there are difficulties in solving the Richards equation,which hinges upon its strong nonlinearity. The coefficients of the partial differential equation, that is to saythe components of the hydraulic conductivity �K ðhÞ, depend on the pore water pressure or moisture con-tent. However, �K ðhÞ can vary over several orders of magnitude for small changes in water content or pres-sure head. Although analytical solutions have been found for one-dimensional forms of the Richardsequation under particular boundary conditions [Parlange, 1972; Philip, 1991b; Srivastava and Yeh, 1991; Iver-son, 2000], a general, analytical closure for this equation has not yet been obtained. Generally, numericaltechniques have been used instead [e.g., Rubin and Steinhardt, 1963; Freeze, 1969].

2.2. Shear Strength Variation in Partially Saturated SoilsThe stability analyses of natural slopes require the evaluation of the destabilizing forces with respect to theshear strength of the soil, s, and the variation of the shear strength itself [Lu and Godt, 2013]. According tothe Mohr-Coulomb failure criterion, in a cohesionless soil the shear strength is proportional to the normaleffective stress r0 [Terzaghi, 1943]:

s5r0 � tan /05ðr2uwÞ � tan /0 (2)

where /0 is the effective internal friction angle and r is the total vertical stress. In defining the effectivestress, Terzaghi only accounted for forces propagating through the soil skeleton. Given the practical rele-vance of the effective stress, many theoretical and practical studies have been undertaken to describe andquantify it. In particular, Bishop [1959], Skempton et al. [1960], Morgestern and Price [1965], and Fredlund andMorgestern [1977] followed a macroscale approach, which constitutes the basis of classical soil mechanics.Such an approach can accurately describe soil behavior under saturated conditions, when the soil-watersystem can be treated as an equivalent continuous medium with macroscopic stresses defined at theboundary. In this framework the pore water, which acts over the entire grain surface, constitutes a neutral,isotropic stress. Therefore, the system can be described by macroscopic stress-state variables such as totalstress, pore water pressure, and intergranular bonding stress, which provides cohesion at zero normal stress.When the water content decreases and the soil begins to desaturate, however, the pore water pressure isno longer a neutral stress in the soil-water-air system. The macroscale variables are no longer adequate todescribe the forces acting on the system since local interparticle forces arise through the different phasesand their interfaces. According to Lu and Likos [2006], these forces are physicochemical forces, surface

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tension, and forces arising from negative pore water pressure. Conceptually, they can be lumped togetherand described through a single macroscopic variable, rs called suction stress, which, together with theeffect of air pressure acting on the dry, hydrated portion of the grain surfaces, ua, can be added into Terza-ghi’s effective stress expression to account for interparticle forces in partially saturated soils. Therefore, theeffective stress principle, under the framework of the suction stress characteristic curve [Lu and Likos, 2006]is expressed by equation (3):

r05ðr2uaÞ2rs (3)

and rs [see Lu and Likos, 2006] is defined in equation (4):

rs5rC01Drpc1rcap1vðua2uwÞ (4)

where rC0 represents the physicochemical stress under saturated conditions, which is used as a reference,Drpc represents the changes in physicochemical stress due to desaturation, rcap is the capillary stress dueto surface tension, and vðua2uwÞ describes the contribution due to matric suction. Matric suction, or simplysuction, is defined as the difference between the air pressure acting on the dry portion of the grain surfacesand the pore water pressure, ðua2uwÞ. Of course, all of these local forces also exist in saturated soil but theyare not necessary in describing the soil stress state, which can be fully described by macroscopic variablesunder saturated conditions. Since suction stress arises from soil desaturation, it is strongly dependent onwater content and matric suction. As such, it is a characteristic function of the soil-air-water system thatallows for the definition of the suction stress characteristic curve, SSCC (Figure 3). The suction stress is anintrinsic function of unsaturated soils that relates the resultant of interparticle physicochemical stresses,capillary stresses, and negative pore water pressure to the matric suction or to the water content [Lu andLikos, 2006]. It can be approximated by equation (5), Lu and Likos [2006], which underlines the dependenceof suction stress on matric suction and relative saturation:

rs52h2hr

hs2hrðua2uwÞ (5)

In this respect, the suction stress approach provides a unified macroscopic representation of the microscopicbehavior of unsaturated soils. Introducing equation (5) into the Mohr-Coulomb failure criterion yields:

sf 5c01ðrn2uaÞf tan /01h2hr

hs2hrðua2uwÞf tan /0 (6)

where c0 is the cohesion at zero normal stress due to the intergranular bonding stress, rn is the total normalstress, ua is the air pressure, uw is the pore water pressure, and /0 is the internal friction angle. The term

c0 05h2hr

hs2hrðua2uwÞf tan /052rstan /0 (7)

represents the apparent cohesion (i.e., the contribution of suction stress to soil shear strength, according toLu and Likos [2006]).

There are various works in literature, such as [Meisina and Scarabelli, 2007; Montrasio and Valentino, 2008;Yeh and Lee, 2013; Lepore et al., 2013], that have used the effective stress equation for unsaturated soilsbased on the [Bishop, 1954] formulation r05ðr2uaÞ1vðua2uwÞ, where v is a coefficient varying between 0and 1. Most of these works have used the Vanapalli et al. [1996] parameterization (v5 h2hr

hs2hr). In this paper,

however, we define the effective stress using the approach based on suction stress, [Lu and Likos, 2006].This approach has unified the description of flow and stress phenomena in all types of soils, ranging fromsand and silt to clay. Also, there is no need to define the coefficient v for effective stress, given that suctionstress is a function only of soil suction. Moreover, unlike previous formulations, the suction stress approachcaptures the nonlinear and peak behavior of the effective stress in sandy and silty soils.

2.3. The Relevance of the Suction Stress Approach to Slope StabilityThe SSCC concept is applied to slope stability analysis to account for interparticle stresses that developthrough changes in water content [Lu and Godt, 2008]. The soil strength required in the computation of theFactor of Safety (ratio of stabilizing to destabilizing forces), FS, is evaluated using equation (6), which hasthe following form when substituted:

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FS5tan /0

tan b1

c0

csZsin bcos b1

c0 0

csZsin bcos b

5tan /0

tan b1

c0

csZsin bcos b2

rstan /0

csZsin bcos b

5tan /0

tan b1

c01 h2hrhs2hr

wcwtan /0

csZsin bcos b(8)

where b is the slope angle, w is the water potential [L], and Z is the soil thickness. Figure 1 provides aninsight into rainfall-induced and stress-variation-induced soil failure mechanisms. Consider a natural, stable,unsaturated slope with an average stress state described by the larger Mohr circle (solid line) in Figure 1. Itsfailure envelope is represented by the straight line tangent to the solid Mohr circle. During a rainfall event,the soil imbibes water and suction stress is reduced, in line with variations in matric suction and volumetricwater content. This corresponds to a downward shift of the failure envelope in Figure 1. Since the failureenvelope in this configuration is secant to the larger circle (original solid line), the soil may fail.

This analysis of soil strength variations in hillslopes is expected to describe the evolution of slope stabilitywithout imposing a specific failure mechanism. It should also accurately reproduce shallow-landslide trig-gering times and locations.

3. The Hydrogeomechanical Model

Many variables and parameters are called into the formulation of equation (8): the slope angle, b, is deter-mined by DEM analysis; the saturated unit weight, cs, is assigned after geological inspection; and soil thick-ness, Z, is given according to the hypotheses and models discussed in section 4. The friction angle, /, andthe cohesion coefficient, c0, are assumed as random variable, whose characteristics are described below.The assignment of the water-related parameters is also described below.

The soil water content, h, and the suction, w, were simulated using the GEOtop model, [Rigon et al., 2006;Endrizzi et al., 2014]. Eventually, the simulated h was considered as the mean value of a random variabletoo, as explained below.

By taking c0; /, and h to be random variables, we state our interest in the probability of failure (i.e., the prob-ability of FS) rather than in FS itself, as given by equation (8). Assuming, therefore, that FS follows a log-normal distribution [Frattini et al., 2009; Duncan, 2000] the probability of failure is:

P½FS < 1�5P½lnFS < 0�5U 2llnFS

rlnFS

� �(9)

where: llnFS5 lnlFS20:5 � r2lnFS

� �;

rlnFS5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffilnð11m2

FSÞp

; lFS and mFS are themean and the coefficient of variationof FS computed using the FOSMmethod; and U is cumulative distribu-tion function of the standard normaldistribution. We assumed c0; /, and has random variables with standarddeviations equal to a percentage ofthe mean values.

The First-Order Second MomentMethod (FOSM) [Dai and Lee, 2002;Baecher and Christian, 2005; Arnoneet al., 2015] is used here to approxi-mate the expectation and variance ofa function of independent random var-iables. It consists in approximating the

Figure 1. Schematic of Mohr circle showing a decrease in soil shear strengthoccurring during a rainfall event. The solid line circle represents the natural stressstate of the slope before wetting, the dashed circle represents the minimumstress state occurring when the soil is saturated. c0 is the cohesion due to theintergranular bonding stress and c00 is the apparent cohesion.

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desired statistic, G5Gðx1; ::; xnÞ, with its Taylor series expansion about the expected (mean) values of ran-dom variables, so that:

E½G�5Gðl½x1�; . . . ; l½xn�Þ (10)

r2½G�5Xn

i51

�dGdxi� r½xi�

�2

(11)

where l½xi� and r½xi� are, respectively, the mean and standard deviation of the random variable xi.

Transient soil moisture, hðtÞ, and pressure heads, wðtÞ, are computed by numerically integrating the Rich-ards equation with GEOtop, as described in Endrizzi et al. [2014]. In the model, equation (1) is discretizedusing a finite-volumes technique. The system of equations for each cell is solved by using a first-order preci-sion, unconditionally stable, Newton-Krylov method. The required relation between suction head, w [L], andvolumetric water content, h [-], that is to say, the soil water characteristic curve (SWCC), is given through thevan Genuchten [1980] parametrization.

The numerical integration of the Richards equation removes the assumption of stationary conditions in sub-surface flows. Therefore, it is possible to describe infiltration-redistribution processes and consequent tran-sient flows, which are of primary importance in landslide triggering.

For three-dimensional simulations, GEOtop is able to consider the influence of topography on water andenergy budgets because it is based on a mesh directly derived from the digital elevation model (DEM) ofthe analyzed basin, which approximates natural slopes, aspect, and curvatures.

GEOtop and the estimation of failure probabilities are run by using different soil moisture conditions andpressure heads computed for each time step. This provides an FS probability that varies in time and space.In addition, the calculation is performed for each layer (into which the soil depth has been discretized) toinvestigate the stability at different depths, after having characterized the soil in geotechnical terms. There-fore FS probability also varies with depth, and the depth of a potential failure is allowed to vary from thesurface to the bedrock without any constraint.

4. Model Application

To assess the impact of topography on transient hillslope hydrology and shallow landslide triggering, we considerthree approximations of real topographies: concave, convex, and planar. They are extracted from 10 m DEM dataof the Friuli region, in the eastern Italian Alps (Figure 2), using the uDig spatial toolbox, Abera et al. [2014]. Thehighly eroded character of the area is mainly due to a large landslide that occurred in 1817, Castiglioni [1962], inresponse to a heavy rainfall event. To isolate the effect of morphology, we assume a constant soil thickness of1.5 m over the entire landscape, which is divided into 30 layers in the model. An impervious layer is located1.5 m below the surface, at the base of the overlying soil. The three morphologies were selected based on theirshape as seen from a 3-D rendering of the topography. Since the operator r2z is the second derivative in spaceof the elevation (z, m) of a site, it represents the concavity/convexity of that site. Planar cells are the ones forwhich r2z50, concave cells have r2z > 0 and convex cells have r2z < 0 [Abera et al., 2014]. Individual hydro-logical and stability-analysis simulations were executed for each of the three different morphologies.

In the study area, many landslides have occurred during and after late summer storms, characterized byintense rainfall. Therefore, we carried out the analyses under similar conditions. We assumed a synthetic12 h rainfall with an intensity of I1 5 18 mm/h, and we ran the simulations for 48 h. The hyetograph shapewas assumed equal to the measured rainfall that triggered a landslide event in the study area. In order tounderstand the role and effect of the rainfall event, we also tested two different events with I2 5 16 mm/hand I3 5 20 mm/h, respectively, and both of 12 h duration. The rainfall intensity I1 should mimic a volumeof rainfall that, on average, is both typical of this area of the Italian Alps and often triggers shallow land-slides. Therefore, we chose an average value for the rainfall intensity within a typical 12 h event. With theaim of assessing infiltration pattern sensitivity to rainfall intensity, we explored two additional intensities I2and I3. This choice was driven by a desire to investigate one variable at a time. Specifically, we wanted toinvestigate the role of morphology on infiltration and, ultimately, on the probability of failure. In the nearfuture, the role of rainfall intensity in this matter will be further investigated in its own right.

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Three different water table depths were set as initial conditions to assess the impact of the antecedent soilmoisture conditions. Water table depths at 1.7, 2.0, and 2.5 m below the surface define the Wet, Medium,and Dry initial conditions, respectively. Based on the water table depth, GEOtop computes a hydrostaticprofile of initial water pressure for the unsaturated zone. Water content is computed accordingly, using asoil water retention curve relationship. For all simulations, the soil has a cohesion of 5 kPa and an internalfriction angle of /0534. The soil unit weight varies with depth according to the water content of each layerunder initial conditions, then it is allowed to vary according to the variation in water content. The soil is ahomogeneous silty sand, characterized by a 1025 m/s saturated hydraulic conductivity and van Genuchtenparameters of n 5 3.5, a 5 0.97 m21, hr 5 0.02, hs 5 0.4 [van Genuchten, 1980]. The soil water characteristiccurve (SWCC) and the soil stress characteristic curve (SSCC) are shown in Figure 3, left-hand and right-handsides, respectively. Soil parameters have been derived from laboratory tests on specimens sampled at theexperimental site. Direct shear tests under field conditions were used to determine the shear strengthparameters of the soils. Standard deviation is used to describe test result variability.

Even though GEOtop is able to simulate infiltration excess overland flow, this runoff mechanism is not themain process taking places in the study area. In fact, the soil types are characterized by saturated hydraulicconductivity (36 mm/h), higher than the three rainfall intensities used in the simulations (I1 5 18 mm/h,I2 5 16 mm/h, and I3 5 20 mm/h). Because the three rainfall intensities are each applied for 12 h, each sce-nario has a different rainfall total input: 216 mm for I1, 192 mm for I2, and 240 mm for I3. Finally, during thesimulation period, we neglected the evapotranspiration effect on the water content dynamic.

5. Simulation Results

The hydrological model, GEOtop, yields maps of pressure head and volumetric moisture content at hourlytime steps for each morphology analyzed. The probabilistic infinite-slope stability model, based on the FOSM

Figure 2. Model domain for basin-scale simulations shown on 10 m resolution, shaded relief map. The representative hillslopes selected formorphological analysis are highlighted in color and labeled. Basin wide elevation ranges from 1000 to 1900 m above sea level. Friuli, Italy.

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method, yields stability maps in terms of probability of failure. Pressure head, water content, and stabilitymaps are output at hourly time steps. We did not use observed soil moisture time-series to evaluate the simu-lated soil moisture dynamics. In the next subsections, we describe: (i) the influence of morphology on transienthydrology at local and catchment scales, considering rainfall I1 and initial condition Medium, (ii) the influenceof morphology on probability of failure considering rainfall I1 and initial condition Medium, and (iii) the influ-ence of hyetographs (I1, I2, and I3) and initial conditions (WET, MEDIUM, AND DRY) on probability of failure.

5.1. Impact of Morphology on Transient HydrologyFigure 4 shows the effects of infiltration on pore water pressure at three locations (P1, P2, and P3) for eachof the concave, convex, and planar morphologies. The three points were selected in the upper (P1), middle

Figure 3. Soil water characteristic curve (left: SWCC) and suction stress characteristic curve (right: SSCC) [Lu and Likos, 2006] for the homo-geneous soil of the case study. The relative van Genuchten parameters are n 5 3.5, a50:97 ½m21�; hr50:02; hs50:4.

Figure 4. Pressure head profiles evolution in time at three given locations (P1, P2, and P3) for concave, convex, and planar topographies,respectively. Different colors represent different time steps (0, 1, 2, 4, 6,12, 24, 48 h from simulation start). The color variation in the mapsrepresents the elevation in meters.

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(P2), and lower (P3) parts of the basins and have similar hydrological and topographic features (total con-tributing area, slope angle, topographic gradient, soil properties). Soil moisture profiles for the same pointsare reported in supporting information Figure S1. Infiltration profiles for the different basin morphologiesare generally similar in shape and values. This is more evident during the initial part of the simulation andfor the upper locations (P1); while during the final part of the simulation and for the lower locations (P3) thepressure head in the concave morphology assumes slightly higher values than in the convex morphology.Moreover, in supporting information Figures S4–S6 we presented the relationship between pressure headand slope for each morphology filtered by the logarithm of the total contributing area. The figures showthat the differences between morphologies appear more evident by increasing the total contributing areaand that below 0.01 km2 the behavior of the three morphologies is quite similar. This confirms that, at localscale, topography has little impact on transient hydrology (at least this is true for the representative mor-phologies and locations selected, i.e., the points P1, P2, P3 on each slope). This is because the flow in theunsaturated zone is mainly vertical (as stated in Iverson [2000]; Lu et al. [2011]) and not affected by laterredistribution.

In contrast, an effect is observed at the catchment scale (Figure 5 and supporting information Figure S2),where pore pressure and water content distributions vary as a function of the slope angle for concave, pla-nar, and concave morphologies. In Figure 5 and supporting information Figure S2, each row refers to a soillayer (0.3, 0.9, 1.2, and 1.5 m deep, respectively) and each column refers to a time step (12, 24, 48 h from

Figure 5. Evolution of pressure head as a function of slope for concave, convex, and planar morphologies, respectively in blue, red andblack dots. Plots are provided for different soil layers (0.3, 0.9, 1.2, and 1.5 m deep) and for different time steps (12, 24, 48 h from simulationstart). Each row represents a given soil layer and each column represents a given time step. Each single plot is labeled: L stand for layer, fol-lowed by the depth of the layer, T stands for time followed by the time at which the plot is referred.

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simulation start). In the figures, the blue, red, and black points correspond to cells of the concave, convex,and planar morphologies, respectively.

For a given slope angle, positive pressure heads and water content are higher for the concave morphology(blue points) than for the planar (black points) and convex (red points) morphologies, respectively. Differen-ces in pore water pressure and in soil water content increase with simulation time and with slope. This high-lights that, although concave morphologies are more prone to collect water than steep morphologies, theeffect of morphology on infiltration and redistribution is quantitatively minimal, particularly in the uppervadose zone. Since, as shown, pressure head values are locally independent of the morphology, differencesin pressure heads at catchment scale, can be attributed to saturated, lateral, subsurface flow. Moreover, thetopographic effect is emphasized in steeper slopes, when the lateral distribution is more significant andconsequently the terrain shape becomes more important.

5.2. Relation Between Changes in Suction Stress and Failure ProbabilityFigures 6 and 7 show the spatial correlation between changes in suction stress and probability of failure forthe concave and convex sites, respectively. Results are reported for five layers (at 0.3, 0.6, 0.9, 1.2, and 1.5 mdepth, respectively) and four time steps (1, 12, 24, and 48 h after the storm beginning). White areas in thesuction stress maps represent the portion of the catchment which is saturated, where the suction stressreduces to zero; colored pixels are unsaturated points, whose value is readable from the color-key. Corre-sponding patterns of instability are illustrated in the maps on the right-hand side in terms of probability offailure. Therefore, red zones in the stability map are associated with a high probability of failure (80–100%),are saturated or near saturation and their relative suction stress is negligible. The suction stress maps in Fig-ures 6 and 7 provide insight into the possible triggering mechanism occurring in this particular case. Theshallow layers, less than 60 cm, do not experience significant increases in soil moisture compared to thedeeper layers at any time step of analysis. This suggests that the increase in soil moisture in deeper layers

Figure 6. Suction stress and probability of failure pattern evolution for the concave site. Plots are provided for different soil layers (0.3, 0.6,0.9, 1.2, and 1.5 m deep, respectively) and for different time steps (1,12, 24, 48 h from simulation start). Each row represents a given soillayer and each column represents a given time step. Each plot is labeled: L stands for layer, followed by the depth of the layer, and Tstands for time, followed by the time step, to which the plot is referred.

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may, for the most part, originate from lateral redistribution. Suction stress, which is tensile in nature (nega-tive values), increases (from negative values toward 0) as the soil wets and vanishes when the soil becomescompletely saturated. As a consequence, shallow landslides result from a relatively rapid increase in soil suc-tion, which reduces soil strength. Figure 8 shows the probability of failure as function of the slope angle forthe 1.2 m layer and the 48 h time step for the convex and concave sites. The colors of the points indicate itssuction stress value. The figure shows how, for a given slope, saturated or near-saturated pixels have ahigher probability of failure compared to unsaturated pixels. This trend is evident for pixels with slope anglegreater that 258, both in concave and in convex sites.

5.3. Impact of Basin Morphology on Slope StabilityTo assess the impact of morphology on slope stability, we quantify the propensity for shallow landslideoccurrence as a function of the slope angle, which is the gradient of the elevation function at any givenpoint. Analyses were carried out for each basin morphology type: concave, convex, and planar. Stabilityanalysis focuses on determining the factors causing landslide triggering (wetness, time, depth, soil geo-mechanical characteristics, etc.). The layering used is a means of discretizing soil depth: slope failure proba-bility is computed independently of each soil layer to identify the weakest depth at which the column ofsoil above that depth would fail. For this reason, as soon as instability occurs in a certain layer of soil weconsider the whole hillslope unstable, even if the shallow layers remain stable. The percentage of unstableareas is computed as the ratio of the area characterized by a probability of failure higher than 0.75 to thetotal area of the basin (with area calculated as number of pixels times pixel resolution).

Figure 7. Suction stress and probability of failure pattern evolution for the convex site. Plots are provided for different soil layers (0.3, 0.6,0.9, 1.2, and 1.5 m deep, respectively) and for different time steps (1,12, 24, 48 h from simulation start). Each row represents a given soillayer and each column represents a given time step. Each plot is labeled: L stands for layer, followed by the depth of the layer, and Tstands for time, followed by the time step, to which the plot is referred.

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Figure 9 shows the probability of failure as a function of the slope angle for concave, planar, and convexbasin morphologies. Each row refers to a soil layer (0.3, 0.9, 1.2, and 1.5 m deep) and each column refers toa time step (12, 24, 48 h from simulation start). Instability occurs at 1.2 m depth and 24 h after the begin-ning of simulation for concave sites. At 1.5 m depth, all three morphologies are unstable; even in this case,however, for a given slope, concave sites have a higher probability of failure.

In general, the failure probability is higher for the concave morphology and this behavior is more evident asthe slope increases. A concave basin morphology can be more vulnerable to shallow landslides than a pla-nar or convex site due to lateral fluxes that are topographically driven toward concave areas. To test thevalidity of this statement, we computed the percentage of saturated area for the three basin morphologiesat 1.2 m depth and 24 h after the beginning of simulation. We used 1.2 m depth because it is the depthwere failure occurred.

Results show that the 32% of the concave basin was saturated versus 27.6% of the convex and 29.7% of theplanar sites. Concave sites are, therefore, prone to collect and store soil moisture, which allows for a greaterincrease in pore-water pressure at the impermeable lower boundary and an increase in the area resultingunstable in the model. This is also confirmed by the percentage of unstable area of each site computed at1.5 m depth for time step 24 h: percentage of unstable areas is equal to 30, 21, and 1.3%, for concave,

Figure 8. Probability of failure in the concave and convex sites as a function of the slope angle for the 1.2 m layer and at the 48 h timestep. The colors of the points represent the suction stress value.

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convex, and planar basin morphologies, respectively. Both in the concave and in convex morphologies, wefound high probability of failure in the upslope parts of the basins. This is explained by high slope angles inthose parts of the basins.

5.4. Impact of Rainfall and Initial Conditions on Slope StabilityThe results presented in the previous subsections are for the Medium initial condition (water table depth at2.0 m) and the I1 (18 mm/h) rainfall rate. In order to investigate the effect of initial conditions and rainfallrate on slope stability, simulations were also conducted using I2 (16 mm/h) and I3 (20 mm/h) rainfall rateand Wet (water table depth at 1.7 m) and Dry (water table depth at 2.5 m) initial conditions. Following thesame procedure presented in the previous section, the percentage of unstable areas is computed for eachscenario by combining each hyetograph (I1, I2, and I3) with each initial condition (Dry, Medium, and Wet).Comparisons of the percentage of unstable areas computed for the nine scenarios are presented in Figure10 for the 24 h time step. A single plot in Figure 10 shows the percentages of unstable area (y axis) for dif-ferent hyetographs (x axis) and for different morphologies: concave (in blue), convex (in red), and planar (inblack). Figure 10 has five rows, one for each soil layer (at 0.3, 0.6, 0.9, 1.2, and 1.5 m depth) and has threecolumns, one for each analyzed initial condition (Dry, Medium, and Wet).

In all scenarios, the percentage of unstable areas for the concave site is higher than those for the convexand planar morphologies. For the scenarios based on Dry initial condition, unstable areas are less than 1%

Figure 9. Evolution of probability of failure as function of the slope for the concave, convex, and planar morphologies, respectively inblue, red, and black dots. Plots are provided for different soil layers (0.3, 0.6, 0.9, 1.2, and 1.5 m deep, respectively) and for different timesteps (12, 24, 48 h from simulation start). Each row represents a given soil layer and each column represents a given time step. Each plot islabeled: L stands for layer, followed by the depth of the layer, and T stands for time, followed by the time step, to which the plot isreferred.

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for all the three morphologies and for each rainfall scenario. For the scenarios based on Medium initial con-dition, the percentage of unstable areas increases with rainfall. Moving from 16 to 20 mm/h, the increase ofunstable areas is higher for concave sites (from 30% to 55%) than for convex sites (from 21% to 30%).

The scenarios based on the Wet initial condition are the most landslide prone. Instability occurs at 0.6 mdepth for almost all the basin morphologies and involves a greater portion of the basins compared to theresults based on Medium scenarios. The lowest intensity rainfall (16 mm/h) combined with the Wet initialcondition triggers instability after 24 h and at 1.2 m of depth. In this case, percentage of unstable areas ismore than 50% for concave morphology, almost 25% for the convex and 1% for the planar.

5.5. DiscussionThe results of this study provide an accurate numerical investigation of how different morphologies effectvariable saturated hillslope hydrology and shallow slope stability. This was previously assessed just by fieldmeasurements and/or empirical models [e.g., Dai and Lee, 2002; Carrara et al., 2003; Dahal et al., 2008].

Our analysis was not limited to a steady state description of subsurface flows and allowed therefore to eval-uate the timing of the failure and the role played by transient rainfall and antecedent soil moisture condi-tions. For control, we also performed a slope stability simulation based on the SHALSTAB model [Dietrichand Montgomery, 1994] presented and commented in the complimentary material. These simulations con-firm the overestimation of the unstable areas that was previously observed in other works [e.g., Casadeiet al., 2003; Lanni et al., 2011]. Literature and our own analysis agree in attributing this overestimation to thesimplification of fluxes dynamics and to the stabilizing effect of soil cohesion and suction stress whichSHALSTAB does not account for.

Differently from previous studies [e.g., Mirus et al., 2007; Simoni et al., 2008; Arnone et al., 2015], we used athree-dimensional hydrological model for solving the Richards equation, carefully modify to manage transi-tion from vadose to saturated conditions, and we implemented the effective stress theory by Lu and Likos

Figure 10. Comparison between percentages of unstable areas computed for time step 24 h. The figure shows the percentage of unstablearea (y axis) for different hyetographs (I1, I2, and I3) and for different morphologies: concave (in blue), convex (in red), and planar (in black).Each row of the figure refers to a different soil layer (at 0.3, 0.6, 1.2, and 1.5 m depth) and each column refers to a different initial conditionconsidered (DRY, MEDIUM, and WET).

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[2006] that provides a unified and mathe-matically consistent description of transitionbetween saturated and unsaturated states.

The hydrological analysis suggests that, in asilty sandy soil for the selected rainfall rates(16, 18, and 20 mm/h, each with a durationof 12 h), and initial and boundary conditions,infiltration is not greatly affected by mor-phology at local scale. Because the watertable rises during the storm event, the satu-rated zone expands upward, generating asaturated flow that moves downslope. Thisresults in an increase in the soil moisturecontent of areas located downslope that isnot only due to rainfall infiltration, but alsoto saturated subsurface flows that flow fromthe catchment crest toward the basin outlet.

The results presented in this paper show that transient pressure heads influence the stress state of soil,inducing variations in suction stress. In particular, the results indicate that a decrease in the absolute valueof suction stresses, due to an increase in pressure head, may induce shallow soil failures. Rainfall infiltrationincreases water content and, as a consequence, the absolute values of both soil suction and suction stressdecrease. However, changes in the stress field only involve shear strength, since the variations in suctionstress are small compared to the vertical effective stress [Terzaghi, 1943]; in addition, the lateral componentof the earth pressure, being proportional to the vertical effective stress, is not significantly affected by thesechanges. This aspect is captured by the numerical solution of the Richards equation implemented in themodel; in contrast, the infinite-slope approach does not describe the effects of morphology on slope stabil-ity as far as the 3-D stress field is concerned. A 3-D slope stability approach should also account for neigh-boring effects on the stability of a single cell due to lateral earth pressure. This would provide insight intothe effects of morphology on the 3-D stress field, showing that, at a given point within the soil mantle, thecontribution of the lateral earth component is larger for a convex slope than for a concave one (Figure 11)because of the greater vertical overburden stress, rv5csoil � hi , generated by a larger soil thickness layingabove a given horizontal datum in a convex slope (AC 5 h2) than in a concave one (AB5h1 < h2). This hastwo opposing consequences, the balancing of which dictates the stability of a given location. Since the lat-eral earth pressure is added to the downslope weight component, it plays a more destabilizing role in aconvex morphology than in a concave one. The counterpart is relative to the soil shear strength, which isproportional to the vertical effective stress r

0v5rv2uw , being uw the pore water pressure [Terzaghi, 1943].

Therefore, given the same overall conditions, the shear strength of a soil in a convex morphology is higherthan in a concave morphology. However, in this case the effect of morphology would be practically time-independent due to small value of changes to suction stress relative to the vertical effective stress (overbur-den stress). If the variation of the earth pressure coefficient with matric suction were considered [Lu andLikos, 2004], then the lateral earth pressure would be theoretically time-dependent.

A constant soil thickness was assumed regardless of the basin morphology, so that morphological effectsare investigated with respect to subsurface fluxes only. The effect of morphology on soil thickness is delib-erately ignored in this study and the results have been interpreted in this context. They do not claim gen-eral validity since they have been found under specific hydrological conditions and for specificmorphologies.

The right-hand side of Figure 3 shows the relation between soil suction (negative pressure head) and suc-tion stress for the silty sand investigated in this work. The curve presents a peak at 1 kPa of soil suction. Thisindicates that there is an optimum value of water content that maximizes the soil strength, providing 6.25kPa of apparent cohesion. The slope is initially stable under the initial water content, which provides theslope with around 4.5 kPa of minimum apparent cohesion. This value is computed considering the maxi-mum water content of the initial condition (0.35), which corresponds to the minimum value of apparent soilcohesion.

Figure 11. Schematic of the different overburden stresses for concaveand convex morphologies. h1 5 AB and h2 5 AC represent the soil thick-ness above a given horizontal datum for a concave and a convex slope,respectively.

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Moreover, in order to show that results are not dependent on the value of rainfall intensity and initial condi-tions used for the simulations, we analyzed the sensitivity of unstable areas to these quantities. The resultsconfirmed that the percentage of unstable areas for the concave site is higher than that for convex and pla-nar morphologies for all scenarios.

6. Conclusions

An analysis was carried out on three different basin morphologies, derived from a 10 m DEM, to investigatethe impact of basin morphology on partially saturated, transient hydrology at catchment scale and, ulti-mately, on slope stability. This analysis suggests that the impact of morphology on transient hydrology isscale-dependent. As shown, it is not greatly relevant at local scale for points having the same hydrologicalfeatures (total contributing area, distance from the divide, slope angle, hydraulic conductivity, van Gen-uchten parameters), where pressure head and water content profiles are nearly identical (Figure 4 and sup-porting information S1). Whereas some more relevant impacts are observed at catchment scale, asdisplayed by the right-hand side of Figure 5 and supporting information Figure S2. Slope stability is affectedby: (i) a decrease in soil suction throughout the whole catchment during a rainfall event; and (ii) by higherwater pressures that build up at concave locations, where water is topographically driven through saturatedsubsurface flows. A transient 3-D numerical simulation has the potential to capture lateral flows and lateralredistribution of soil moisture both in the short and long-term. The landslide triggering time can be pre-dicted more reliably through an improved description of the pressure redistribution. This can be done byincorporating the effect of the unsaturated zone and by implementing a probabilistic approach, which pro-vides failure patterns and probability, as presented in Figures 6 and 7.

Additionally, the study shows the correlation between a decrease in soil effective stress and slope instability,providing a physical explanation for the shallow landslides that are often observed during and after high-intensity storms. In steep slopes (with internal friction angle greater or similar to the slope angle), where thesoil is held in place by capillarity (tensile suction stress), an increase in soil moisture content, due to rainfallinfiltration, may build pore water pressure and reduce the soil shear strength. Results show that, despitepartially saturated subsurface flow not being affected significantly by morphology at local scale, morphol-ogy has an effect on the total subsurface flow and on slope stability at catchment scale.

The infinite-slope assumption, implemented in the model, neglects mechanical effects of three-dimensionallandslide geometry. This introduces an approximation which could bias the physical understanding of shal-low landslide triggering. Further effort is required to advance the physical understanding of shallow land-slide triggering at watershed scale in a fully 3-D, time-dependent context.

Last, future work could examine the effects resulting from the hydraulically anisotropic character of soils;methods could include observations of soil water content and suction. Indeed, the results provided in thepaper may be used to guide future monitoring efforts, needed to provide a more comprehensive validationof the results and conclusions reported.

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